In many terrestrial-based communications waveforms, frequency offsets—whether caused by hardware imperfections or Doppler caused by relative motion—can generally be assumed to be small. This is due to both the typical rate of motion for most terrestrial-based vehicles, as well as the frequency bands most commonly used to achieve reliable communications. Although these frequency errors can be significant enough to fully degrade successful demodulation, assumptions can be made that reduce the complexity of the error correction. For some simple waveforms, a Phase-Locked Loop or Costas Loop intended to correct phase offsets may be able to compensate for a typically small amount of frequency offset. More complex waveforms, such as Orthogonal Frequency-Division Multiplexing (“OFDM”) may require data-aided (“DA”) compensation, but typically they assume a frequency offset small enough to still enable accurate detection of their pilot tones.
As the radio frequency (“RF”) spectrum becomes more saturated, forcing waveforms into higher bands, the effects of Doppler will be more pronounced. High speed aircraft, such as military jets, communicating at extremely high frequencies, can push the effects of Doppler beyond the limits of compensation by conventional means. Spacecraft may be subjected to the effects of Doppler at several orders of magnitude greater than aircraft. These effects may be so great that the Doppler shift may be several hundred times larger than the bandwidth of the waveform itself. A spacecraft in Low Earth Orbit (“LEO”) may transition from one extreme of negative frequency Doppler shift to the other extreme of positive frequency Doppler shift while expecting to maintain a constant communication link at every degree in between. A receiver capable of maintaining the instantaneous bandwidth necessary to observe the entire potential Doppler spectrum will suffer from massive Signal-to-Noise Ratio (“SNR”) degradation that may render carrier recovery difficult-to-impossible when exposed to poor channel conditions potentially caused by bad weather.
Existing techniques for Frequency-Locked Loops include the following. The first method (referred hereafter as the “Band Edge” method) is described in Multirate Signal Processing for Communication Systems by Fred Harris, especially Section 13.4, “Modem Carrier Recovery,” as well as Fred Harris et al., “Band Edge Filters Perform Non Data-Aided Carrier and Timing Synchronization of Software Defined Radio QAM Receivers,” Wireless Personal Multimedia Communications (WPMC). The 15th International Symposium on Wireless Personal Multimedia Communications, 24-27 Sep. 2012, pp. 271-275, IEEE, Piscataway, N.J. USA. In essence, the Band Edge method involves streaming the In-phase (I) and Quadrature (Q)components of a complex baseband RF signal in parallel through a positive edge Finite impulse Response (“FIR”) filter and a negative edge FIR filter. These filters are designed to represent the derivative of the matched filter of the target waveform. A comparator is used to determine which filter output has the most energy, and, in a simplified description, the difference between the two is directly proportional to the frequency error. By using a loop filter controlled feedback loop, the frequency error drives a numerically controlled oscillator (“NCO”) that mixes the error frequency with the incoming waveform to drive the incoming signal to baseband. This method has several advantages: 1) the derived frequency error is directly proportional to the carrier offset; 2) frequency correction can be performed on every new sample of data, allowing for rapid carrier acquisition; 3) the technique can track frequency changes without losing lock, as might occur with changes in relative motion or imperfections in the radio frequency (“RF”) front end. However, it has a few disadvantages that make it unsuitable for all occasions: 1) due to the band edge filters' direct relationship with the matched filter, as described, the band edge frequency-locked loop (“FLL”) cannot compensate for frequency errors much more than twice the waveform bandwidth; 2) the filters can be modified to track wider frequency errors at the expense of accuracy; 3) at low SNR, the noise element of the signal greatly disrupts the frequency detector's ability to discern the frequency offset of the signal, resulting in an unstable output frequency that can (and does) greatly disrupt further demodulation of the waveform.
The majority of “frequency-locked loops” in the literature actually refer to phase-locked loop “PLLs”), which are useful for driving an input signal to match a specific phase and frequency of a reference signal. Phase-locked loops are versatile, and can correct for minor frequency offsets. In many conventional systems, the frequency error introduced by Doppler is small enough to be corrected by a phase-locked loop with a broad loop bandwidth. In more sophisticated systems, a PLL can be employed with a broad loop bandwidth for coarse frequency correction, and then switch to a narrower loop bandwidth once frequency is acquired. Such techniques are also not suitable of situations in which the frequency offset is several times the bandwidth of the signal or in low SNR environments.
Some techniques involve directly computing Doppler compensation at the receiver or the transmitter via a look-up table or other comparable means. Such techniques are likely the most capable of rapidly synchronizing with a waveform, and may be critical for high data rate, bursty transmissions. These techniques require several assumptions, however. For instance, in these situations, at least one platform is typically immobile. In some situations, such as satellite communications, one platform has a known flight profile which can be used to compensate for Doppler effects through pre-calculations. Other techniques may require a complicated system of direction finding and inertial sensors to calculate the expected Doppler compensation in near-real time. Because a flight profile may not always be known in advance, multiple nodes may be moving, and/or the cost, size, weight, or power requirements to facilitate a more adaptive inertial system may be prohibitive, these techniques are not suitable for all occasions.